Categorical crystals for quantum affine algebras

Masaki Kashiwara, Euiyong Park

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


In this paper, a new categorical crystal structure for the quantum affine algebras is presented. We introduce the notion of extended crystals Bg(∞) for an arbitrary quantum group Uq(g), which is the product of infinite copies of the crystal B(∞). For a complete duality datum D in the Hernandez–Leclerc category Cg0 of a quantum affine algebra Uq (g), we prove that the set BD(g) of the isomorphism classes of simple modules in Cg0 has an extended crystal structure isomorphic to Bbgfin(∞). An explicit combinatorial description of the extended crystal BD(g) for affine type A(1)n is given in terms of affine highest weights.

Original languageEnglish
Pages (from-to)223-267
Number of pages45
JournalJournal fur die Reine und Angewandte Mathematik
Issue number792
StatePublished - 1 Nov 2022


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